Asymptotics for fractional reaction diffusion equations in periodic media

In this paper, the Cauchy problem for a class of reaction diffusion equations are considered with nonlocal interactions in periodic media. First, we demonstrate the existence and uniqueness of solutions that are both positive and bounded for the stationary equation. Second, we derive results concern...

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Main Authors: Yu Wei, Yahan Wang, Huiqin Lu
Format: Article
Language:English
Published: AIMS Press 2025-02-01
Series:AIMS Mathematics
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Online Access:https://www.aimspress.com/article/doi/10.3934/math.2025177
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author Yu Wei
Yahan Wang
Huiqin Lu
author_facet Yu Wei
Yahan Wang
Huiqin Lu
author_sort Yu Wei
collection DOAJ
description In this paper, the Cauchy problem for a class of reaction diffusion equations are considered with nonlocal interactions in periodic media. First, we demonstrate the existence and uniqueness of solutions that are both positive and bounded for the stationary equation. Second, we derive results concerning the existence and uniqueness of solutions for the Cauchy problem by using the semigroup theory. Finally, we analyze the behavior of the solutions to the Cauchy problem for large times by using the comparison principle.
format Article
id doaj-art-f0a0890398d54be98d3f034da2fb2fa0
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issn 2473-6988
language English
publishDate 2025-02-01
publisher AIMS Press
record_format Article
series AIMS Mathematics
spelling doaj-art-f0a0890398d54be98d3f034da2fb2fa02025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-02-011023819383510.3934/math.2025177Asymptotics for fractional reaction diffusion equations in periodic mediaYu Wei0Yahan Wang1Huiqin Lu2School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, ChinaSchool of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, ChinaSchool of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, ChinaIn this paper, the Cauchy problem for a class of reaction diffusion equations are considered with nonlocal interactions in periodic media. First, we demonstrate the existence and uniqueness of solutions that are both positive and bounded for the stationary equation. Second, we derive results concerning the existence and uniqueness of solutions for the Cauchy problem by using the semigroup theory. Finally, we analyze the behavior of the solutions to the Cauchy problem for large times by using the comparison principle.https://www.aimspress.com/article/doi/10.3934/math.2025177generalized fractional laplacianconvolutionsemigroup theoryasymptotics
spellingShingle Yu Wei
Yahan Wang
Huiqin Lu
Asymptotics for fractional reaction diffusion equations in periodic media
AIMS Mathematics
generalized fractional laplacian
convolution
semigroup theory
asymptotics
title Asymptotics for fractional reaction diffusion equations in periodic media
title_full Asymptotics for fractional reaction diffusion equations in periodic media
title_fullStr Asymptotics for fractional reaction diffusion equations in periodic media
title_full_unstemmed Asymptotics for fractional reaction diffusion equations in periodic media
title_short Asymptotics for fractional reaction diffusion equations in periodic media
title_sort asymptotics for fractional reaction diffusion equations in periodic media
topic generalized fractional laplacian
convolution
semigroup theory
asymptotics
url https://www.aimspress.com/article/doi/10.3934/math.2025177
work_keys_str_mv AT yuwei asymptoticsforfractionalreactiondiffusionequationsinperiodicmedia
AT yahanwang asymptoticsforfractionalreactiondiffusionequationsinperiodicmedia
AT huiqinlu asymptoticsforfractionalreactiondiffusionequationsinperiodicmedia